Temporal aggregation of Markov‐switching financial return models

In this paper we investigate the effects of temporal aggregation of a class of Markov‐switching models known as Markov‐switching normal (MSN) models. The growing popularity of the MSN processes in modelling financial returns can be attributed to their inherited flexibility characteristics, allowing for heteroscedasticity, asymmetry and excess kurtosis. The distributions of the process described by the basic MSN model and the model of the corresponding temporal aggregate data are derived. They belong to a general class of mixture normal distributions. The limiting behaviour of the aggregated MSN model, as the order of aggregation tends to infinity, is studied. We provide explicit formulae for the volatility, autocovariance, skewness and kurtosis of the aggregated processes. An application of measuring solvency risk with MSN models for horizons larger than 1 year and up to 10 years from the baseline U.S. S&P 500 stock market total return time series spanning about 50 years is given. Copyright © 2008 John Wiley & Sons, Ltd.